The Nazcan figures – computer graphics?

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Nezavisimaya gazeta, Igor Alexeev, September 28, 2011

Nowadays there’s hardly a person who wouldn’t have heard about the lines and the drawings in the desert of Nazca. Thousands of perfectly straight and incredibly large truncated triangles, enormous amount of accurate spirals and unusual in design drawings were carved in the times immemorial at the surface of the desert and at the flat highlands near the Peruvian town of Nazca. They can only be seen from a great height. This notion remains to be a mystery for almost one century now (the official discovery of the Nazca lines dates back to 1927). All of the existing hypotheses, including the official taking stand on the religious-ritual origin, do not provide an exhaustive explanation of this phenomenon.

The desert of Nazca is an extremely arid territory located at the western coast of the South America in 45 kilometres of the Pacific Ocean. At present, it is commonly known about the several dozens of geometrically accurate lines and figures at the plateau, but this is probably just a small share of what time and human activities have left to us (the lines are believed to date back to 400 BC-600 AD).

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To the left it is a part of the plateau located near the river Ingenio. To the right is the edge of a big platform located to the South of the plateau. The stones were taken away from the light-coloured surface of the desert, which led to formation of the clearly defined borders that can be visible from the satellites.

Apart from the geometric images there are many other drawings in the area. However, the majority of them are the primitive drawings and remind the images at the ceramics and the textile of Nazca – a culture that existed here 1 500 years ago. They are drawn at the slopes of the hills and can be well seen from the ground.
There also exist other images, which I’m going to tell about.

They differ from the primitive Nazca drawings in the following: the number of these drawings is rather scarce – around 30-40; they are drawn at the surface of the desert and there is no other way to see them, but from an aircraft; they are performed in a completely different manner than those pertaining to Nazca. There is another feature – while the ancient Nazca people mainly depicted the man-like Gods, these drawings do not contain any anthropomorphic images, but depict either plants or animals, or the intricate geometric constructions.

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A geometric construction near the town Palpa. At the photo to the right one can see its central part. One can see that the drawing is laid out with stones on top of the already existing lines. A sketch reproduction was done with the help of several photographs taken from the different angles. The size of the drawing is around 240 meters in diameter. It may as well be a part of a larger construction.

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Several drawings from the desert of Nazca. The length of the biggest image at the plateau – the one reminding of a pelican – is 380 meters (in the centre). For comparison see Boeing-747 in the bottom right corner.

In the framework of a certain research there arose a need to make the sketches of these drawings in a graphic program. The results were the following. All of the drawings (hereinafter we will only talk about the images of plants and animals) are made with one uninterrupted line which has its beginning and its end; the drawings are very well aligned as to their axes; the drawings are congruous – even the slightest deviation would lead to a significant loss of proportions. Maria Reiche, a German mathematician who devoted almost 50 years to the studying of the lines and the drawings of Nazca, wrote in her book “Mystery on the Desert”: “The length and the direction of every section were thoroughly measured and fixed. Approximation would not be enough to make such impeccable outlines which we are now able to see with the help of the aerial photo coverage, as the deviation for only few inches would distort the proportions of an image. The photos allow to imagine what did it cost to the ancient architects to create these wonders. The ancient Peruvians must have had the equipment that is not available even to us nowadays and the knowledge which was thoroughly concealed from the conquerors as the only treasure that they could not have stolen”.

For Maria Reiche the roundings and the elegant curves of the drawings presented a particular interest. At the first glance, this feature is of no importance. But it turned out that all the roundings of the ancient drawings were performed with the mathematically calibrated curves. Indeed, to draw such a curve at a sheet of paper is rather complicated while doing this on the grounds is difficult even for the geodesists with the modern equipment.

When working with these images it appeared that while applying the “Bezier curves” – one of the main tools of any graphic program – the program would often do the similar outlines autonomously afterwards. The Bezier curves were developed by a French engineer specially for the purpose of the car design and they have a rather complex mathematical description. If we look around, we see that the more modern and the more prestigious the car is the more curves – sophisticated and elegant Bezier curves – it has in its design. Nowadays, due to the wide application of the computer based project design, the Bezier curves are used more and more often in architecture, technology, etc. And it is these Bezier curves that appeared to be the main tool for the images at the plateau. The most sophisticated drawing in the desert of Nazca – the spider – seems to have been solely compiled of the Bezier curves.

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The outline of “the spider” in a graphic program with application of the Bezier curves.

If to look at the 300-meter proper curve depicting the goiter of “the big pelican” – the biggest drawing in the desert – which, by the way, is very well seen in Google satellite maps, then there remains no more doubt as to the ability of the ancient architects to perform the mathematic operations necessary for reproduction of such outlines. Otherwise, as Maria Reiche suggested, it might also be that they used some unknown to us tools to make this.

And another interesting detail. One can notice that the images are not symmetrical. The symmetry is infringed not in the direction of distortion or violation of proportions, or mistakes – it brings certain liveliness into the rigorous graphic images.

This was perplexing at first – why would someone make his or her life more difficult during the transfer of the drawings from a sketch to the ground’s surface? There’s already enough trouble with the Bezier curves there. But then it became evident – the ancient drew the projections of the 3-dimensional images. In other words, the ancient were taking into account the notion of perspective. There was an attempt to reproduce the creature which is called “the nine fingers”. As a result, a funny beast turned out. It is not similar to anything in the world, but it looks rather natural. Perspective is considered in more or less all drawings.

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Reproduction of “the nine-fingered being”.

How is it possible that the Indians – a small ancient nation at the earliest stages of social  development that had no central power, that knew no script, that left no traces of the lay-out marking for these drawings – how could they be in charge of this art? This remains a mystery. Why the images are so few and why were they so ruthlessly crossed out or even destructed by other lines? What could explain such a queer design of the drawings and why can they only be observed from a great height? And why there exist no images of Gods at the slopes of the hills, while they are so widely represented at the textile and the ceramics of Nazca? Maybe because these were the Gods, whom the Indians depicted at the ceramics, who did those drawings just for fun?

 

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